Abstract

If (T) over cap : (X) over cap --> (X) over cap is a two-sided subshift on a finite number of symbols and T : X --> X is the corresponding one-sided subshift we give a necessary and sufficient condition for a continuous function (f) over cap : (X) over cap --> R to be cohomologous, with respect to ((X) over cap, (T) over cap), to a continuous function which can be defined on X. The property of being cohomologous to such a 'one-sided' function is important in the study of equilibrium states because there are extra tools, such as the Ruelle transfer operator, for one-sided systems. We present the results in the more general context when T : X --> X is a continuous surjection of a compact metric space and (T) over cap: (X) over cap --> (X) over cap is its natural extension, and look at the special case of subshifts. We also prove some related results and give applications to subshifts.

Due to unforeseen circumstances, several corrections were missed from the published version of the above paper. The corrected paper is reprinted in its entirety below. Taylor & Francis apologise for the errors